Help me please find the break-even quantity

E

edy21

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So the problem is the following:

The price of a pizza is 18. Your pizza place has fixed costs of 10000 and a cost of a pizza is 14.

a) How many pizzas do you need to sell to break-even?
b) How many pizzas do you need to sell for a profit of 2000?

Apparently this is how you resolve a) :

P*Q=FC+AVC*Q
18Q=10000*14Q
Q=2500

My question here is, how do we get Q=2500?

And b) :

Profit=P*Q-(FC+AVC*Q)
2000=18Q-(10000+14Q)
Q=3000

Same question how do we get Q=3000?

Your help would be very much appreciated!
 
Profit \(P\) is revenue \(R\) less costs \(C\). If \(Q\) represents the quantity of units produced and sold, then

[MATH]P(Q)=18Q-(14Q+10000)=4Q-10000[/MATH]
To find what quantity results in a particular profit, we equate the profit function to that profit and solve for \(Q\).

a) To break even, this means profit is 0:

[MATH]0=4Q-10000[/MATH]
[MATH]4Q=10000[/MATH]
[MATH]Q=2500[/MATH]
b) For a profit of 2000, we use:

[MATH]2000=4Q-10000[/MATH]
[MATH]4Q=12000[/MATH]
[MATH]Q=3000[/MATH]
 
MarkFL said:
Profit \(P\) is revenue \(R\) less costs \(C\). If \(Q\) represents the quantity of units produced and sold, then

[MATH]P(Q)=18Q-(14Q+10000)=4Q-10000[/MATH]
To find what quantity results in a particular profit, we equate the profit function to that profit and solve for \(Q\).

a) To break even, this means profit is 0:

[MATH]0=4Q-10000[/MATH]
[MATH]4Q=10000[/MATH]
[MATH]Q=2500[/MATH]
b) For a profit of 2000, we use:

[MATH]2000=4Q-10000[/MATH]
[MATH]4Q=12000[/MATH]
[MATH]Q=3000[/MATH]
Click to expand...

Thank you so very much, you have my gratitude!
 
Let's see, you buy a pizza for $14 and sell it for $18. So you make $4 profit per pizza. The problem is that you have this $10,000 fixed cost. Boy are you going to have to make an awful lot of $4s to cover that $10,000 expense. Let's see 4 +4 + 4 + 4 + 4 + ... + 4 =10000. Do you now see why you need to sell 2500 pies to break even?
Now you want to make $2000 profit. At $4 profit a pizza you will need to sell 500 pizzas---Plus the 2500 that paid for the $10,000 fixed cost.
 
A lemonade stand might be in order. That's about as far as my business skills extend.

-Dan
 
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